Richard Swinburne's Inductive Argument for the Existence of God – A Critical Analysis

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LINKÖPINGS UNIVERSITET

Department of Culture and Communication

Independent thesis Advanced level (degree of Master (One Year)) Tutor: Bo Petersson

Author: Emma Beckman Word count: 46 287

ISRN: LIU-IKK/PF-A-09/001--SE

Richard Swinburne's Inductive

Argument for the Existence of God

–

A Critical Analysis

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Linköpings Universitet, Filosofiska Fakulteten

Linköping University, the Faculty of Art and Sciences

Institutionen för kultur och kommunikation (IKK) Avdelningen för filosofi

Department of Culture and Communication (IKK) Philosophy

Projekt: Magisteruppsats, Praktisk filosofi

Project: Bachelor thesis, Practical philosophy

Titel: Richard Swinburne's Inductive Argument for the Existence of God – A Critical Analysis

Title: Richard Swinburne's Inductive Argument for the Existence of God – A Critical Analysis

Författare: Emma Beckman

Author: Emma Beckman

Handledare: Bo Petersson

Tutor: Bo Petersson

Sammanfattning: Denna uppsats diskuterar och kritiserar Richard Swinburne’s induktiva argument för Guds existens. I sin The Existence of God, försöker Swinburne visa att Guds existens är mer trolig än inte. Detta argument tar alla traditionella

argument för Guds existens i beräknande.. Swinburne använder de fenomen och händelser som utgör premisser för dessa argument som bevis i ett försök att visa att hans hypotes är mer trolig än inte. Han genomför detta genom att använda sig av Bayes teorem. Syftet med denna uppsats är normativt – att bedöma styrkan I Swinburnes argument för Guds existens. Mina primära invändningar mot Swinburne är att han använder sig av ett subjektivt sannolikhetsbegrepp, att han förlitar sig allt för starkt på enkelhet som en förklaringsmässig dygd och att hans Gudsbegrepp inbegriper en inkoherent bild av Guds natur. Jag ifrågasätter den faktiska framgången i Swinburnes projekt, och även vad Swinburne hade kunnat fastställa om hans projekt hade varit framgångsrikt.

Abstract: This essay discusses and criticizes Richard Swinburne‘s inductive argument for the existence of God. In his The Existence of God, Swinburne aims at showing that the existence of God is more probable than not. This is an argument taking into consideration the premises of all traditional arguments for the existence of God. Swinburne uses the phenomena and events that constitute the premises of these arguments as evidence in an attempt to show that his hypothesis is more probably true than nor. Swinburne pursues this task by way of

applying Bayes' theorem. The aim of this essay is normative – to judge the strength of

Swinburne‘s argument for the existence of God. My primary objections towards Swinburne is that he professes a subjective concept of probability, that he relies too heavily on simplicity as a virtue of plausible and probable hypotheses and that his concept of God involves an

incoherent picture of God‘s nature. I question not only the actual success of Swinburne‘s project but what his argument, if it had been successful, would have been able to establish.

Nyckelord: Swinburne, Bayeseanism, Gudsbevis, Förklaring

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ACKNOWLEDGEMENTS

First and foremost, I would like to thank my supervisor, professor Bo Petersson. Without your devoted help and guidance, I would never have been able to finish this project. You are a true inspiration. I would also like to thank my family, my best friends Johan and Isabella, and everyone else who stood by me and believed in me. I love you.

Emma Beckman Linköping, March 2009

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A. INTRODUCTION

I. What is the subject of this essay?

The subject matter of this essay is Richard Swinburne‘s natural theology – his inductive argument for the existence of God. In this essay, I discuss and criticize his argument as presented in The Existence of God1 and summarized in ―Arguments for the Existence of God‖2

. The Existence of God carries a misleading title, indicating that Swinburne claims to prove the truth of the claim that God exists. In this respect, ―Arguments for the Existence of God‖ is more informative. Swinburne‘s aim in these works is to provide an argument for – not a conclusive proof of – the existence of God. Although he does believe this hypothesis to be true, he makes it clear that he considers any attempted proof of this to be in vain –

―although reason can reach a fairly well-justified conclusion [by rational argument] about the existence of God, it can reach only a probable conclusion, not an indubitable one‖3. Thus, he treats the question he sets out to answer – (a) ―whether the evidence of human experience shows that the claim [of theism] is true or that it is false‖4

– as equivalent to (b) ―whether the balance of all the relevant evidence favours the claim of theism or not‖5

. Thus, (b), rather than (a) will also be the main topic of this essay.

Giving the central question this interpretation, Swinburne assumes that it will be provided an affirmative answer – that is, that the hypothesis of theism will be shown to be more probable than not – through formulation of what he refers to as a good P-inductive a posteriori argument for the existence of the God of theism. This is an argument taking into consideration the premises of all traditional arguments for the existence of God.

Swinburne pursues his task by way of a twofold evaluation of these arguments. First, he investigates, for each one of the arguments whether it adds anything to the probability of the existence of God – whether it is a C-inductive argument or not. Second, he takes the phenomena and events that constitute the premises of these arguments as evidence in an attempt to formulate a P-inductive argument for the existence of God by application of Bayes‘ theorem. Broadly speaking, this is Swinburne‘s method. His line of reasoning follows a simple structure, of which the most important claims are as follows:

All worthwhile arguments for the hypothesis of theism – the hypothesis that the God of theism exists – h, are inductivea posteriori.

According to the method of inference to the best explanation, some phenomenon or event E is explained if the explanation – such as h – is simple and has high predictive power.

All relevant arguments for h are cases of inference to the best explanation – claim that the occurrence of some E is reason to suppose that h is true since h provides the best explanation of E. Each one of these arguments increases the probability of h.

1

Swinburne, The Existence of God (2nd ed.), Oxford University Press, Oxford 2004

2

Swinburne, ―Arguments for the Existence of God‖ in Milltown Studies, Vol. 33, 1994, p. 24-36. Sebastian Rehnman‘s Swedish translation of this article was published in Filosofisk Tidskrift, No. 4, 2007, p. 26-40.

3

The Existence of God, p. 2.

4

ibid., p. 1, my italics.

5

ibid., p. 13. The hypothesis of theism is that the God of theism exists. The interpretation of this hypothesis is not entirely clear. It is sometimes phrased as the more elaborate ―that the Universe exists because there is a God who keeps it in being and that the laws of nature operate because there is a God who brings it about that they do‖ (―Arguments for the Existence of God‖, p. 28). Note also that (b) makes the task less demanding than (a) in that it does not require that we reach conclusive

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Among the arguments against the existence of God, merely one – the argument from evil – decreases the probability of h.

These arguments ‗add up‘ – taken together, the premises of these arguments make h, and thus the existence of God, probable.

Stated this way, the core claims of Swinburne‘s argument are in need of not only justification but also definition and clarification. It is thus a first task of this essay to seek a coherent understanding of his argument6.. The main task, however, is normative – to judge the strength of Swinburne‘s argument for the existence of God. Plainly speaking, the primary aim of this essay is not merely to convince the reader that Swinburne goes wrong in his argument, but to show how and why I consider this so obviously being the case. My primary objections

towards Swinburne is that the concept of probability he professes is subjective, that he relies too heavily on simplicity as a virtue of plausible and probable hypotheses and that his concept of God involves an incoherent picture of God‘s nature. These three points throws doubt not only on the actual success of Swinburne‘s project but on what his argument, if it had been successful, would have been able to establish.

II. Why is this essay important?

Swinburne‘s argument deserves serious attention for a variety of reasons. Whether or not God exists is indeed one of the most important questions that stir the human mind7. Although the particular question he sets out to answer is not phrased in entire equivalence to this, his argument – if successful – has implications for our ways of understanding and discussing the issue. I take it to be an implicit claim of Swinburne‘s that his argument brings with it a

closure of the debate between atheism and theism. If the theistic hypothesis is such that it may at most be defended in probabilistic terms and if, further, Swinburne‘s argument is successful, there is simply nothing left to say regarding the issue. This would provide a strong reason to re-write textbooks of Religious studies, Philosophy of Religion and the like, adding a passage stating that the debate of the existence of God came to an end with the publication of the first edition of The Existence of God. More importantly however, the success of his argument would have great implications for our view of the world and our place in it. It would make us unwise (or even instrumentally irrational) not to live according to Gods supposed will8. I do not consider it an exaggeration claiming that the success of Swinburne‘s argument would force a change of our entire conception and understanding of us as human beings.

If, on the other hand, Swinburne‘s argument does not succeed, he has no legitimate grounds for claiming that God exists. Although one must provide good arguments for one‘s position, independently on whether one approves of or rejects the claim of theism, I think that the burden of proof rests heavier on the shoulders of people – such as Swinburne – claiming that God does exists. I take it to be a more or less general view within contemporary

philosophy that, as an application of (something similar to) Occams razor, one shall not postulate any ―new‖ entities without providing some good reasons for this.

6

As presented in ―Arguments of the Existence of God‖ and The Existence of God. Since many of the questions merely alluded to in ―Arguments for the Existence of God‖ are elaborated in The Existence of God, I will focus on the latter.

7

It is symptomatic that Harry J. Gensler puts this very question at the top of his list of ―ultimate questions of life‖ in an attempt to define the subject of Philosophy to students touching upon the subject for the very first time. (Gensler, Ethics: a

contemporary introduction, Routledge, London 2002, p. 2)

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III. What is the purpose of this essay?

i. What questions will not be answered?

Working out his argument for the hypothesis of theism, Swinburne touches upon various topics9 – including the mind-body problem, objectivity of ethical and aesthetic value and rational agency10. Although topics raise questions important and legitimate in their own respects, I will not get go into any lengthy debate with him on these issues. This is due, first, to the limited space allowed for this essay and, second, the advantages of focusing at one thing at the time. Making the scope of this essay too broad, I am risking that none of the questions gets the fair treatment it deserves. For the same reasons I have decided, also, not to go into general debate over the specific arguments for and against the existence of God. My treatment of these arguments will, thus, be confined to Swinburne‘s handling of these.

ii. What questions will be answered?

As should be clear by now, this essay is a discussion and criticism of Swinburne‘s inductive argument for the existence of the theistic God as he has presented it in The Existence of God, ―Arguments for the Existence of God‖ and (to some extent) Faith and Reason. The essay has three interconnected aims of which the third takes precedence:

1. Provide a clear presentation of Swinburne‘s argument 2. Point out the problems inherent in it

3. Assess the force of the argument

iii. Disposition

This essay starts off with a presentation and evaluation of the theoretical11 aspects of Swinburne‘s argument. This will be the instrumental part of the essay. I distinguish two aims12 of Swinburne‘s project, of which one may be described as ―subjective‖ and the other as ―objective‖. I challenge his restriction of the arguments to be considered in the discussion of the existence of God. To my mind, the restriction is inappropriate, even in the light of his own aim. The remaining parts of this first section of the essay is devoted to Swinburne‘s method of formulating an inductive argument. I scrutinize his ―logical‖ concept of probability, his view on evidence in general and his way of dividing it into background knowledge and new evidence in particular. I provide some general remarks on the concept of probability and distinguish two ―levels‖ of subjectivity – strong and weak subjectivity – applicable to interpretations of the concept of probability and argue that Swinburne‘s concept is at least weakly subjective. Moreover, I spell out and analyse his concepts of C- and P-inductivity as well as his application of Bayes‘ theorem. Lastly, I state some objections towards his cumulative method and argue that given his concept of probability and his method of

9

Especially in those parts of his argument where he works out his methodological ground.

10

Concerning the mind-body problem, the view commonly referred to as ontological dualism is inherent in Swinburne‘s argument – but never explicitly motivated. Some of Swinburne‘s further claims, such as his denial of the possibility of reducing (what he refers to as) ‗personal explanations‘ to scientific such, rests heavily on his ontological dualism. Concerning aesthetic and ethic values, he professes a view most commonly referred to as realism, or perhaps a supernaturalism (usually defined as the semantic theory that ―X is good‖ means ―God desires X‖). Moreover, I will not judge whether Swinburne‘s account of the arguments renders them properly ―traditional‖ or in what ways they differs from previous formulations, and so on. It is probable that some of his claims seems controversial in the eyes of scholars within religious studies, but this is not the place to establish this.

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or methodological.

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formulating an inductive argument, the calculated probability of the hypothesis of theism bears a necessary connection to some subject performing this calculation.

Having drawn up a clear picture of Swinburne‘s method, I proceed to present and discuss his concepts of ―explanation‖ and, respectively, ―God‖. In this conceptual part of the essay I point at some problematic aspects of his understanding of these concepts. I focus my discussion of Swinburne‘s concept of God upon God‘s ―contingent necessity‖ which I consider incoherent. My discussion of arguments to the best explanation centres upon Swinburne‘s view of explanatory virtues – especially that of simplicity. I argue that he puts too much weight in hypotheses satisfying this criterion and that he underestimates the importance of fit with background knowledge.

The third part of the essay is called ―Analysis‖. These few sections evaluates Swinburne‘s application of the method described in the essay‘s previous part. I analyse his treatment of the different arguments for the existence of God and challenge his claim that each one of these adds something to the probability of this hypothesis. I also argue that Swinburne does not appropriately appreciate the weight of the argument from evil. Having that done, I go on to present the second step of Swinburne‘s argument – his use of Bayes‘ theorem as a tool for judging the probable truth of the hypothesis of theism given the premises of the relevant arguments for the existence of God.

In the fourth part of the essay I state my verdict of the success of Swinburne‘s project. My conclusion will be that he has not succeeded in showing that it is on balance more

probable than not that God exists. It is clear that Swinburne himself is convinced of that God exists. I argue that this is what he, at most, will be able to establish.

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B. INSTRUMENTAL PART

1. Relevant Arguments

1.1. Good, traditional, inductive a posteriori arguments

Swinburne‘s limitation of arguments worthy of consideration in the debate over the existence of God is based upon the claim that in general, the purpose of arguments is ―to get people, in so far as they are rational, to accept conclusions‖13. I take this to indicate that part of his project consists in intellectually convincing rational people that God probably exists. It is however clear that he, in addition to this, wants to show that it is – as an objective matter of fact – probable that God exists. Interpreting Swinburne‘s aim this way makes it important to determine what relative weight he assigns its parts and how he coordinates them. Whereas people may be convinced by bad arguments, the task of determining the probability that God exists places a stricter demand on arguments to be good and relevant. Obviously, they must be based upon true premises.

Given this, it comes as a slight surprise that Swinburne assumes that there is a strong connection between the convincing power and relevance of arguments. In his view, relevant – that is, good – arguments are always ―traditional‖ in the sense that they reflect what,

historically, has provided ―ordinary people‖ with reasons for maintaining or denying the existence of God. Second, the premises of a relevant argument must (a) necessitate or probabilify the conclusion, (b) be known to be true by those arguing over the conclusion and (c) report what are, in some general sense, features of human experience14.

According to (b), an argument for the hypothesis of theism is relevant only if its premises are true and this is known by those who reject15 as well as by those who believe in it. Criterion (c) restricts the class of relevant arguments to what Swinburne refers to as ―a posteriori arguments‖16. He defines ―a priori arguments‖ as ―arguments in which the premises are logically necessary truths—(...) propositions that would be true whether or not there was a world of physical or spiritual beings‖17

. The class of traditional a priori arguments include versions of what is commonly referred to as ―the ontological argument‖ and

arguments claiming that there is something incoherent in the supposition that God exists. Swinburne waves off ontological arguments as mere philosophers‘ arguments that fail to ―codify any of the reasons that ordinary people have for believing that there is a God‖18

and claims to having shown in his The Coherence of Theism that theism is a coherent claim. His view, thus, on what constitutes a relevant argument is neatly summed up in the following few lines:

I do not believe that there is any force in a priori arguments for the existence of God (...). Worthwhile arguments are a posteriori (...). I do not think that there are any sound deductive a posteriori arguments for the existence of God.19 13 ibid., p. 6, my italics 14 ibid., p. 8 15

I avoid the term ―atheist‖ since I consider it unclear what propositions are to be viewed as agreed upon within this group.

16

That is, arguments claiming that human experiences provides grounds for believing that there is, or is not, a God (ibid.) Given that Swinburne uses the concept of a posteriori in an epistemological sense, this amounts to the claim that it is necessary, for the relevance of an argument, that its premises are believed on grounds of human (sensory) experience.

17_ibid. 18

ibid., p. 9

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1.2 Swinburne’s exclusion of deductive and a priori arguments

As I indicate above, there are reasons to question the connection between an argument‘s being traditional or convincing and its being good or relevant. There is no guarantee that those arguments that have historically been appealing in the view of ordinary people are the most convincing or best arguments.20 For all we know, it might be that people historically have been believing in the existence of God for various bad reasons21 – arguments irrelevant not only for the aim of showing that it is probable that there is a God but also for that of reaching a closure of the debate over this question. In other words: I consider it being preferable to focus upon the best arguments – even in the light of the aim of convincing people.

Second, criterion (b)‘s central reference to the beliefs of the people debating is problematic22 in the sense that it seems to make it impossible to formulate a conclusive argument. Since beliefs change over time23, the propositions today satisfying (b) might not do so tomorrow. If the premises of arguments allowed any weight in this debate are necessarily bound to24 the beliefs of people at a specific period of time, any argument may at most function as a temporary proof of the existence or non-existence of God. Furthermore, this restriction on the premises of relevant arguments is too strong. Since people in general have very diverse beliefs, it is perfectly coherent to suppose that the beliefs of people standing on the same side of the debate at some specific time are so diverse that the question of the existence or non-existence of God is the only one concerning which they agree.25

Third, there are reasons to question Swinburne‘s account of what he refers to as ―a priori arguments‖. The concept of a priori knowledge refers to knowledge that does not depend on evidence from sensory experience26. If one is to apply this to arguments, the most appropriate way of doing this is by viewing a priori arguments as arguments in which the constituting propositions (that is, the premises as well as the conclusion) are held true

independently of experience. I do not consider it appropriate understanding the concept of an ―a priori argument‖ as referring to arguments the premises of which are necessary truths. The reason for this is that the epistemological concept of a priori knowledge may not be reduced to that of necessary truth. As has been pointed out by Saul Kripke (among others) we do have a priori knowledge of some contingently true propositions27. Even if it would have been the case that concepts refer to the same set of propositions, it would have been unjustified

reducing ―knowledge a priori‖ (an epistemological concept) to ―necessary truth‖ (a logical or metaphysical concept) – they refer to different kinds of properties of propositions.

Fourth, I consider Swinburne‘s argument for excluding deductive arguments from consideration weak. His distinction seems to be based upon the claim that the premises of a deductive argument make the conclusion certain, whereas those of an inductive argument in some sense support, confirm or give strength to the conclusion28. His reason for excluding deductive arguments from consideration is that all arguments satisfying criterion (b) – that of

20

There many problematic aspects of Swinburne‘s argument (characterized above) for excluding a priori and deductive arguments from the forthcoming discussion. For reasons of space, there is no way of stating them all here.

21

The way I see it, a common (perhaps even the most common) reason for belief in the existence of God is that one has been brought up into this. When this is the case, the person in question may be said to believe in this claim for reasons of authority.

22

This passage is not an argument towards a general epistemological scepticism. The problem, as I see it, is the fact that the contingent beliefs serves such a central role of the criterion discussed.

23

This, I contend, is true not merely of the class of debaters presently existing, but also of the members of this class understood in a broader sense to include all past, present and (perhaps) future people debating this question.

24

Or marked by.

25

Consider the fact that the group of people denying the existence of the God of theism includes, among others, Hindus and Buddhists. Whereas Hindus generally believe in many Gods, but no theistic God, Buddhists claim that there is no God.

26

Moser, Paul K: ―A priori‖ in Craig, E. (ed.), Routledge Encyclopedia of Philosophy. http://www.rep.routledge.com.lt.ltag.bibl.liu.se/article/P001SECT1 4/5 2008-10-06

27

ibid.

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containing merely propositions generally agreed upon – are of the inductive kind. However, the question whether an argument is of the deductive or inductive kind has everything to do with the relation between its premises and conclusion, and little to do with the nature of its premises. That is, one may not disqualify deductive arguments on grounds referring to the properties of their premises. On the other hand, the question whether an argument is to be classified as a priori or a posteriori depends upon the nature of its premises. Thus, if all deductive arguments were a priori and we accepted criterion (c) – that of being a posteriori known – on the premises of good arguments, it would have been justified to exclude all deductive arguments from consideration. However, it is simply not the case that all deductive arguments take a priori know propositions as their premises. Also, the fact that inductive arguments are incapable of providing conclusive proof of the truth of hypothesis does make them inferior to deductive arguments in cases where we aim at the truth. As should be clear by now, Swinburne‘s aim is not to provide a conclusive answer to the theistic question. However, I do believe that investigations should be guided by such aims, at least in the sense of not making such conclusions impossible. This is why I contend that when deductive arguments are available, one does better relying less heavily upon inductive arguments, or at least not entirely excluding deductive arguments from consideration.29

As a last point, it is unclear how we are to understand the claim that none of the deductive arguments for the existence of God satisfies criterion (b). Is Swinburne claiming that (1) among those arguments traditionally put forward in the debate, all the deductive ones start from premises presently not generally agreed upon, or that (2) it is a necessary feature of deductive arguments in this context to start from premises not (ever) generally agreed upon? According to (1) it is possible that future debaters not only to agree on the premises of our present deductive arguments but also formulate new deductive arguments starting from premises at that time accepted by the people on both sides of the debate30. According to (2), it is altogether impossible to formulate a logically valid argument for or against the existence of God that has common items of knowledge as its premises. At first glance, the latter

interpretation may seem far-fetched, but in the light of the fact that a valid deductive inference always has its conclusion contained within its premises31 – this claim may be of benefit for Swinburne‘s argument. Emphasizing this peculiarity of deductive inferences, it seems that such an argument for the hypothesis of theism will need to assume the existence of God already in its premises32. Given this and that God‘s existence is not necessary, deductive inferences are of a poor help for someone who wants to prove that God exists. The deductive method allows merely for conclusions concerning what is possible or impossible.

Propositions claiming something to exist are contingent. The fact that it is possible that God exists does not imply that he does exist, but if it is impossible that God exists, he cannot and does not exist. In other words: it may be proved by deductive inference that God does not exist, but never that God does exist.

I will not state a final verdict on this passage is to be interpreted. Although I do consider Swinburne‘s criteria on relevant arguments to rest upon weak ground, my wish to move on analysing his argument for the hypothesis of theism requires me to temporarily accept them. I do however contend that these problems cast some doubt upon the legitimacy of Swinburne‘s project.

29

Note that I am not saying that one should exclude inductive arguments from consideration. Rather, I think that inductive as well as deductive arguments shall be given their fair attention.

30

This also allows for the possibility that at some time in the past, the debaters (a) had deductive arguments (other than those now available) the premises of which they agreed upon or (b) agreed on those premises which today‘s debaters disagree.

31

In the sense that nothing may be in the conclusion that is not stated in the premises. Swinburne views deduction as a ―mode of inference useful only for drawing out the consequences of what we are already committed to‖. (―Arguments for the Existence of God‖, p. 23)

32

Obviously, one is not bound to accept this view, and it needs to be further analysed what it means for one to ―take for granted‖ the existence or non-existence of God within the premises of some argument.

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2. Formulating a probabilistic argument

2.1. Interpretations of the concept of probability

There are three mathematical axioms of elementary probability theory, applying to all concepts of probability discussed in this essay33.

1. Probabilities are less than or equal to 1. 2. If an outcome is necessary, its probability is 1.

3. If outcomes q and s are mutually exclusive, then the probability of (q or

s) is the sum of the individual probabilities of q and s, that is; P(q v s) = P(q) + P(s).34

―Probability‖ may be interpreted as either a physical or an evidential concept – as a matter of frequency or as a measure of the degree to which some evidence supports a hypothesis. The distinction between these two interpretations is usually held to be that probability as physical concept measures characteristics of sets whereas it as an evidential concept measures

characteristics of sentences or propositions35. The degree of support referred to within the evidential interpretation may be subjectively interpreted as representing degrees of belief – dispositions to act36. Swinburne alludes to this distinction when he claims to use an inductive concept of probability (which he claims to be a measure of the degree of support some hypothesis is provided by its evidence) to be distinguished from what he refers to as a statistical account (measuring the proportion of things within some class sharing some property, that is, belonging to some second class).

Swinburne claims to use the method of (quantitative) confirmation theory – a method for ―probabilistically evaluating hypotheses in the light of an increasing number of

evidence‖37

. Within this method, lower-case letters (p, q, and r) represents propositions or conjunctions of such, so that P(p|q) represents the inductive probability of hypothesis p, given evidence q – for example the probability of Albert Einstein‘s General Theory of Relativity given all reports of relevant observations and experiments. Since Swinburne does not want his concept of probability to contain any reference to agents, he is keen to mark the distinction between his concept – that of logical probability – and various subjective such.

It seems that when Swinburne talks about a statistical account of probability, he has that concept which is commonly referred to as the relative frequency or empirical

interpretation of probability in mind. On this physical concept, measures of probability refers to ―the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out‖38

. Given this interpretation, the probability of an event E is equal to E‘s long-run relative frequency when the experiment is carried out many times:

If an experiment is repeated n times, and E occurs r times, the relative frequency, rf, of E = rfn(E) = r/n.39

33

The aim of this paragraph is to present those aspects of those concepts of probability relevant for the present discussion.

34

I earn this account to Horwich, Paul: Probability and Evidence, Cambridge University Press, Cambridge 1982, p. 17 and Talbott, William, Probability Laws in Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/epistemology-bayesian/supplement1.html 2008-08-29

35

Lewi, I.: ―Statistical and Inductive Probabilities by Hugues Leblanc‖ in The Journal of Philosophy, No. 1 1963, p. 22

36

Most commonly, these dispositions are analyzed in terms of betting behavior. (see Horwich, p. 19)

37

Kupiers, Theo: ―Confirmation Theory‖ in Craig, E. (ed.), Routledge Encyclopedia of Philosophy; http://www.rep.routledge.com.lt.lag.bibl.liu.se/article/Q015?ssid=834741359&n=1#

38

Easton, Valerie J. & McColl, John H.: ―Statistics Glossary‖ http://www.stas.gla.ac.uk/steps/glossary/probability.html 2008-06-16

39

ibid. This view sometimes embodies the additional idea that ―the probability an A (…) would be an O (…) is equal to the limit of the relative frequency of Os in an infinite random sequence of As‖ (Horwich, Paul: Probability and Evidence, Cambridge University Press, Cambridge 1982, p. 43) This is often viewed as problematic since it seems to assume the observation of an infinite sequence of trials or experiments.

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In his Probability and Evidence, Paul Horwich spells out four subconcepts or interpretations of ―probability‖ – the empirical, subjective, rationalist and logical interpretation. Each one of these interpretations is based upon what he refers to as ―the primitive theory‖ of probability, according to which:

[T]he probability that a trial or experiment will have a certain outcome is equal to the proportion of possible results of the trial which generate that outcome. There are six possible results of throwing a di[c]e, and three of these yield an even number; so the probability of that outcome is ½.40

The above account of relative frequency and the primitive theory demonstrates the division between physical and evidential concepts. The relative frequency account presupposes an empirical investigation in the sense that any calculation of probability involves actual numbers collected through repeated experiments. Accordingly, it is an a posteriori matter to calculate probabilities, making probability an objective measure. The primitive theory, on the other hand, is phrased in (what may be referred to as) a hypothetical manner41, allowing calculations of probability to be performed prior to experiment. This suggests a view of probability as having to do with a priori predictions and expected outcomes, which implies a subjective concept. Generally, within subjective views, probability reports ―a person‘s level of expectation for a hypothesis or event‖42, thus measuring something ―in the mind‖ of a

subject43_{. Horwich suggests the following definition:}

The subjective interpretation: an attribution of some probability to as statement is an expression of the speaker‘s degree of confidence in its truth.44

I will hereafter refer to this as strong subjectivity. Claiming this concept to reduce probability to a matter of taste, Horwich formulates two additional concepts, which ―although not

empirically testable, (...) are allegedly logical truths expressing a sort of partial entailment relation between statements.‖45

These a priori concepts both derive from the primitive theory:

The rationalist interpretation: an attribution of some probability to a statement is a claim to the effect that, given the evidential situation, it is reasonable to believe, to a specified degree, that the statement is true.46 The logical interpretation: statements of the form ‗the probability of A relative to B is x‘ are claims about the degree to which the truth of B would support A.47

Although none of these concepts involves strong subjectivity, it is clear that both do contain a necessary reference to some subject or agent. This is the same as saying that they involve what I will from now on refer to as weak subjectivity48. I am going to argue that the concept of probability employed by Swinburne is in close resemblance to the latter of the above

interpretations – that is, the logical interpretation. Contrary to what he wants to claim, I do take his concept of probability to involve if not strong, then at least weak subjectivity.

40

ibid., p. 16

41

Note that Horwich even uses the concept of possibility in his account of the primitive theory.

42

Strevens, Michael: ―Notes on Bayesian Confirmation Theory‖;

http://www.nyu.edu/gsas/dept/philo/user/strevens/classes/Conf06/BCT.pdf 2008-06-16

43

Jeffrey, Richard : ―Subjective Probability – The Real thing‖; http://www.princeton.edu/~bayesway/Book*.pdf

44 Horwich, op cit., p. 18 45 ibid. 46_ibid. 47 ibid., my italics.

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According to Horwich, the logical and rationalist interpretations of probability ―indicate (without explicitly expressing) the degree to which someone, whose total knowledge consists of B, should believe in A‖49. Accordingly, any claim about the probability of a specific statement is a claim about what a fully rational agent should believe. The assumption that the degrees of belief of ideally rational persons conform to the mathematical principles of

probability is fundamental to the Bayesian framework50. According to Horwich, this approach derives ―from the view that the concept of subjective probability is of fundamental value in reaching an understanding of scientific methodology‖. I take these remarks to suggest that a Bayesian approach to probability does assume at least weak subjectivity. If this is where we find Swinburne – as I will argue – this also provides a clear conception of what, in his mind, constitutes a convincing argument.

2.2. The logical probability of p on q

As I state above, Swinburne is eager to portray the relation he has in mind as differing from the general case of subjective probability. He stresses that P(p|q) is an objective measure of probability – that it is a concern with how probable q makes p ‖apart from who is doing the calculation, (...) [that is: apart from the] degree of confidence [the agent has] in the evidential force of q‖51. Further, he points out that his concept of probability makes the probability of p given q an a priori measure:

If q represents all the relevant evidence, the value of P(p|q) cannot depend on further evidence—it measures what the evidence you have already got shows. It is an a posteriori matter whether, in 1,000 tosses, 505 have landed heads; but an a priori matter whether that evidence gives a probability of 0.505 to the next toss landing heads.52

This account confirms what is claimed in the previous section – that the logical probability of p given q is a hypothetical figure. Moreover, the above remarks reveal that we are dealing with an evidential concept of probability. It brings into the light the fact that this concept of probability contains weak subjectivity. Although lacking explicit reference to some agent, the last cited passage does presuppose some agent or subject. The reason for this is that (a) it is a matter of a priori assessing the probability, given knowledge, observations and experiments53 q, that p takes place in the future, and (b) q is to include all relevant54 evidence. These remarks point in a forward direction, towards Swinburne‘s calculation of the probability of the hypothesis of theism given the evidence provided by the arguments picked out as relevant for and against the existence of God.

In the above case, we are asking for the probability of the next toss of a coin landing heads. There are two possible outcomes (events), of which one is the sought after outcome, and there is a known number of previous tosses of which a certain (also known) number have generated that outcome. Given some additional premises such as ―the world is regular and predictable‖, ―both outcomes are equally probable‖, ―the dice is perfectly balanced‖, ―the dice

49

ibid.

50

The particularities of which I describe below.

51

The Existence of God, p. 15

52

ibid., p. 16, my italics.

53

Below, I discuss the subjectivity inherent in observations and reports of such, and the fact that ―evidence‖ is always evidence according to some agent

54

I take the restriction to ―relevant‖ evidence to imply that the content of q has been picked by some subject, trough the means of some procedure. This procedure is subjective in the sense of being based upon different features of some subject, such as knowledge and beliefs concerning the way the world functions. Because of this, I take it to be at least partly a matter of subjective judgement to pick out, among all observations and experiences, those relevant for the calculation of P(p|q). It is possible that Swinburne would reply, when faced with this objection, that this is a mere practical problem having to do with the capacities of the person performing the calculation – that this would not be a problem for the person rightly qualified. Claiming this, however, is to assume moral realism.

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will not be worn out by repeated experiments‖, the a priori judgement of the probability that the next toss lands heads comes off as inherently simple55, making it plausible to assume that people will agree on the matter. These features of the case may lead some to claim the judgement to lack any measure of subjectivity. Disregarding appearances, the similarity of different people‘s judgements and the simplicity of the calculation do however not suffice to remove the subjective element from the set-up. In order to see this, consider the similar case where the number of possible outcomes is (close to) infinite, the sought after outcome is by necessity a matter of interpretation and there are no previous experiments done. Such a set-up not only removes the simplicity of establishing the a priori probability of the sought after outcome, but also makes it easier coping with the fact that P(p|q) is a matter of subjective judgement at least in the weaker sense. The latter set-up serves as a fitting description of cases where we want to calculate – that is, assess – the probability of events involving agents, actions and intentions. In other words, this is a more suitable description of the kind of events the probability of the occurrence of which we presently want to establish.

2.3. The subjectivity of background knowledge and new evidence

Swinburne divides the content of q of P(p|q) – the ―evidence‖ available to some observer – in two parts, e & k. Since this division plays an important role for Swinburne‘s argument, I will let his own words speak on the matter:

It is often useful to divide the evidence available to an observer into two parts—new evidence and background evidence; if this is done, the former is represented by e and the latter by k. Background evidence (or background

knowledge, as it is sometimes called) is the knowledge that we take for

granted before new evidence turns up56.

This makes it clear that the contents of e and k may vary for some agent A investigating the probability of p, depending on the surrounding circumstances. It also confirms that P(p|q) is a hypothetical measure, stating the support q would provide p in case q was a true statement. In order to get a full understanding of what Swinburne has in mind here, we do however need a more extensive account of these concepts. Swinburne spells out what we are to include in e and, respectively, k by formulating an example with a murder-investigation:

h could represent the hypothesis that Jones did the murder; e could represent

the proposition that reports all the new evidence that detectives discover—for example, that Jones‘s fingerprints were found on the weapon, that he was near the scene of the murder at the time it was committed, etc., etc., k could represent the proposition reporting the detectives‘ general knowledge about how the world works—for example that each person has a unique set of fingerprints, that people who touch metal and wood with bare hands usually leave their fingerprints on them, etc., etc. Then P(h|e & k) represents the probability that Jones did the murder, given detectives‘ total evidence.57

It is important to note the immediate connection between some observer or judge – some subject – and the contents of (e & k). In the example, (e & k) represents the set of total evidence available to each one of the detectives investigating whether Jones committed the murder. Let us assume there are two detectives investigating the case, so that (e & k)1 refers to

the total set of evidence available to the first detective and, (e & k)2, to the total set of

evidence available to the second detective. Moreover, let U be some proposition referring to the fact that each person has a unique set of fingerprints and N some proposition referring to

55_{To the effect of making it resemble that of calculating relative frequency!} 56

ibid., my italics.

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the fact that Jones was near the scene of the murder at the time it was committed. The way the example is put, we are bound to assume that for both (e & k)1 and (e & k)2, k includes U, and

e includes N. We need however not assume (e & k)1 and (e & k)2 to be identical. Also, it need

not be assumed that U and N are necessarily included within the total evidence available for any possible observer. It is a matter of contingency that N is included in the class of

observational evidence e and U, respectively, in the background knowledge k, for both detectives. Clearly, there are people who have never heard of things such as fingerprints. In other words, it could have been the case that although there was someone (except Jones), who knew that Jones was near the scene of the murder at the time it was committed, the detectives did not know this, so that N was not included within e for any of the detectives. If this were the case, N would still (in some ―objective‖ sense) have constituted a fact relevant for calculating the probability that Jones did commit the murder. That is, all other things being equal, some other observer – some third detective – for whom e did include N, would in that case have been able to do a better, more correct, assessment of the probability that Jones committed the murder.

Second, since both detectives know and take for granted U, they must in some sense have learned58 it – it would be absurd claiming the fact that everyone has a unique set of fingerprints to be known a priori. This means that the class of propositions taken for granted by a specific observer is apt to change over time and that it is a matter of contingency that the detectives know U. These remarks seem to apply to many facts we take for granted in our understanding and interpretation of the world. It should, moreover, be plain that e stands for propositions referring to facts the knowledge of which is based upon sense-experience (observation). These propositions are furthermore claimed by some agent to constitute evidence of h. This, then, is yet another reason for arguing that the nature and content of e depends in a direct way on a subject – an agent. There is no such thing as a disinterested reception of objective raw data or reports mediating facts about the state of things. I agree with Lars-Göran Johansson‘s discussion of observation and linguistic reports of such in his Introduktion till Vetenskapsteorin, where he argues the point that observations are necessarily bound to some agent. First, observations are concrete, active actions. He uses examples from the natural science to point out the presence of a subjective element even in measurements of time59. Second, the stimuli on our sense organs constituting the ―raw data‖60 are always processed by the agent. This processing activity is governed by the earlier experiences, attention, mental conditions, expectations and the like of the agent. I consider it trivial that linguistic reports of observations are bound to some language, which in turn is modelled in accordance with our conception of the world. This makes up a third reason for claiming that observations and reports of such are necessarily bound to some agent.

I take these three points to show that given a logical interpretation of probability, the contents and formulation of (e & k) is always relative to some agent performing the

calculation. The features of (e & k) depend on not merely who is performing the calculation but also on when he or she is performing it61. In the murder case, this means that P(h|e & k) is a measure of how probable the total set (e & k) of relevant knowledge held by the detectives makes h. In other words P(h|e & k) tells us how probable h is for the detectives. To me, this does not say much about the actual, objective probability of h. Even without claiming that P(h|e & k) is a measure altogether ―in the mind‖ of the detectives, in the strong sense of subjectivity, I consider it clear that this measure relies on components that are, making it a case of weak subjectivity.

58

I am using this word in its most wide application, including ―being told by mom‖ as a way of learning.

59

Being a kind of automatic process, such judgments are to be distinguished from the interpretation necessarily connected to ―meaningful phenomena‖ – phenomena containing or indirectly constituted by intentional phenomena.

60

If there is such a thing

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2.4. The importance of background knowledge

Another relevant issue connected to Swinburne‘s division of the class of evidence has to do with his treatment of the class of background knowledge, k:

The division between new evidence and background evidence can be made where you like—often it is convenient to include all evidence derived from experience in e and regard k as being what is called in confirmation theory mere ‗tautological evidence‘, that is, in effect all or other irrelevant knowledge.62

The passage speaks for itself – in Swinburne‘s opinion, k is to refer to a class of irrelevant knowledge. Later on, he adds to this that the contents of k ―can be ignored‖63. I take this to imply that when we judge the probability of the existence of God given all relevant evidence, it is justified to exclude from consideration all but the observational evidence.

Note that the division of the evidence into e and k Swinburne makes here, must be taken to differ from the division made in the case of the detectives. There is no way of including the fact that each person has a unique set of fingerprints and that people who touch metallic things with their bare hands usually leave their fingerprints on them in k if this is to refer to a class of propositions the knowledge which is independent of experience. That is, given Swinburne‘s principle for dividing evidence, this knowledge would have to be included within e rather than k, as was the case in the example with the detectives.

What kinds of facts, then, will be included within k if we apply this way of dividing the evidence? As we will see later64, it is possible interpreting the division between e and k as that between (1) e and facts known before e (k), where e is a proposition referring to some state of affairs, phenomenon or event claimed to constitute evidence of the hypothesis in question. However, it seems most plausible interpreting Swinburne as making the distinction between (2) a priori knowledge (k) and all evidence derived from experience (e). Contained within the class of a priori knowledge are mathematical, logical and geometrical facts. Disregarding whether this is his own view or if he merely adapts an already established procedure of evaluation, I consider it highly disputable claiming such facts to be irrelevant. Also, his use of the term ―tautological‖ as referring to a priori known facts is highly unfitting, even confusing. I cannot get to my mind what Swinburne is aiming at by using this term. For this reason I will avoid the concept of ―tautological evidence‖ as far as possible in the

remainder of this essay.

2.5. Hypothetical evidence of hypotheses

According to the above account of what Horwich calls the ―logical interpretation‖ of probability, this measures the degree to which some statement B would support some other statement A, given the truth of B. On this account, the probability of A on B is a measure independent of whether either of the statements are (known to be) true, so that B may be referred to as ―evidence‖ of A in a mere hypothetical or theoretical sense. If B is a statement expressing a proposition e referring to a state of affairs, phenomena or event E the truth of which would make probable the truth of the statement A expressing some proposition

referring to some other state of affairs, phenomena or event H, it makes no difference whether E has actually taken place. In order to argue that this is the correct way of understanding Swinburne‘s concept of probability65

, I will examine his view of the relation between a

62

ibid., p. 17

63_{ibid. This is discussed more thoroughly in the section on Swinburne‘s formulation of a cumulative argument.} 64

In the section on the components of Bayes‘ theorem

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proposition constituting some hypothesis h and a proposition e referring to some state of affairs, phenomena or event, which is claimed to be evidence of h. It is important to keep in mind that e and h are propositions referring to state of affairs, phenomenon or events E and H. These propositions are expressed by statements such as A and B, above. There is no one-one correspondence between any given e and some specific single phenomena, state of affairs or event E. Rather (given that h always refers to the hypothesis of theism as specified), the contents of e and k may vary, which it is important that they are carefully defined.

It is a central claim of Swinburne‘s that if some hypothesis h successfully predicts some state of affairs, phenomena or event E, this makes probable the truth of h. It is

commonly assumed that if the truth of some h is to be proved this way, the E which e refers to must actually have happened66 – that the proposition e referring to E must be (known to be) true. Swinburne denies this, taking the logical probability of p on q to be an a priori

established, hypothetical figure. In connection to stating his interpretation of Bayes‘ theorem, he claims it to be ―a matter of indifference, as regards the theorem, whether e is observed before or after the formulation of h‖67. Surely, the theorem may be applied nonetheless. What is important to keep in mind here, is not to take Swinburne literary when he refers to (e & k) as ―evidence‖ of h or to P(e|h & k) as the ―predictive power‖ of h with regards to e. That is, Swinburne is not implying that E has ever been observed to occur. For this reason, it may be argued that the logical concept of probability is especially fitting for Swinburne‘s project. Since the evidence of his hypothesis is such that it is hard or even impossible to establish its interpersonal or objective truth68, it may be to his advantage taking h to predict e merely in a hypothetical manner – making the question of e‘s actual truth if not irrelevant then at least uninteresting. I take this to be reflected in Swinburne‘s claim that

it is in itself no objection to the hypothesis that there is a God, that it does not yield predictions such that we can know only tomorrow and not today, whether they succeed. The theist‘s evidence may render this hypothesis probable without this condition being satisfied69

2.6. C-inductive and P-inductive arguments

Three central claims of Swinburne‘s is that all the ―relevant arguments‖ for the hypothesis of theism may be stated as inductive arguments, that most of these arguments will be

C-inductive and that taken together, the premises of the arguments form a P-inductive argument for this same hypothesis. In order to define these concepts, he states that for background knowledge k, new evidence e and hypothesis h:

(…) an argument from e to h will be a correct C-inductive argument if (and only if) P(h|e & k) > P(h|k), and a correct P-inductive argument if (and only if) P(h|e & k) > ½.70

According to this, an argument from evidence e to hypothesis h is a correct71 C-inductive argument if (and only if) the premises increase the probability of the conclusion – that is, if (and only if) the probability of h given the total evidence (e & k) is higher than the probability of h given merely the background knowledge k. Also72, an argument from e to h is correctly 66 taken place 67 ibid., p. 69 68

Since, as I argued above, the propositions e involves a necessary connection to some observer. Moreover, the e of the traditional arguments refers to some state of affairs, phenomena or event of dubious character, such as the occurrence of miracles, revelation or other religious experience

69

ibid., p. 70

70_{ibid., p. 17} 71

That is, is correctly referred to as a C-inductive argument.

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C-inductive iff. e is more likely to occur if h is true than if h is false. An argument is P-inductive if (and only if) all evidence taken together makes the hypothesis probable – if (and only if) e and k makes the probability of h higher than ½. Note, however, that both relations assume that P(h|k) > 0 since if the formulation of h makes it impossible that h is true, the probability of the truth of h cannot be raised by any e73. Given previously stated elementary axioms of probability theory and Swinburne‘s logical concept of probability, it follows that it is true of all propositions p and q that:

P(p|q) = 1 if (and only if) q makes p certain—for example, if q entails p (that

is, [if] there is a deductively valid argument from q to p); and P(p|q) = 0 if (and only if) q makes ~p certain—for example, if q entails ~p. P(p|q) +

P(~p|q) = 1. So if P(p|q) > 1/2, then P(p|q) > P(~p|q) and it is[,] on q[,] more probable that p than that ~p.74

Certainly, if p may be deduced from q, the occurrence of q makes certain that of p. Given that (1) every possible p represents a (declarative/assertive) proposition, (2) q represents all the relevant evidence, and (3) for any formulation of p, necessarily either p or ~p75 it follows that (4) it is necessarily the case that if P(p|q) > ½, then necessarily P(p|q) > P(~p|q).

The way I understand (2), this amounts to the claim that no matter what further (new) evidence is added to q, the value of P(p|q) and P(~p|q) will be the same. Given that I am, further, correct in taking P-inductive arguments to be arguments where P(p|q) > ½, the logical equivalence between [P(p|q) > ½] and [P(p|q) > P(~p|q)] implies, that (5) any

argument from q to p where the probability of p given q is greater than the probability of ~p is a P-inductive argument for p. This means that (6) in order for some evidence q to make p probable, q must support p to a greater degree than it supports its negation, and equivalently, if some evidence q makes p more probable than ~p, q makes p probable. There is however no such restriction on C-inductive arguments. Since in order for q to increase the probability of p in this sense, there need not be any ―special‖ relation between p and q, it makes no difference to the question whether there is a C-inductive argument from q to p that q increases the probability of both p and ~p.76

There is an assumption implicit in Swinburne‘s concept of P-inductivity, important to spell out. This is the assumption that if we may formulate a P-inductive argument for some proposition p this means that p is probable period. In other words, the fact that the probability of p given this evidence is higher than ~p means that p is probable period. In an ordinary case, assuming this would be to confuse two different questions – (a) whether h is probably true and (b) whether given some specific proposition (or combination of such) the probability of h is higher than that of ~h. In this context, however, the q of P(p|q) is supposed to represent all the relevant evidence.

My previous arguments having to do with (a) the necessarily subjective character of the contents of q and (b) Swinburne‘s logical concept of probability, puts a restriction on what one may draw out of these logical relations. Concerning (a) I claimed that since the

formulation and contents of q (or e and k analogously) presupposes a subject, P(p|q) (or P(h|e & k) analogously) is subjective at least in the weak sense. In connection to (b) I argued that any measure of the probability of p on q, given Swinburne‘s interpretation of this

concept, is a measure of some hypothetical support between two statements. Given this, if the

73

This is neatly pointed out by J.L Mackie in his The Miracle of Theism, Oxford University Press, Oxford 1982 p. 97

74

Swinburne op. cit., p. 16-17, my italics

75

Since for any formulation of p it is necessarily the case that [(p v ~p) & ~(p & ~p)], which means that: (a.) either p or ~p is true, and (b.) it is not be the case that both p and ~p are true, and (c.) it is not the case that neither p nor ~p is true. Note also that this is implied by (1).

76_{This highlights the discussion of the previous section – that ―evidence‖ must be provided a mere hypothetical interpretation}

in this connection, making Swinburne‘s concept of evidence diverge from the everyday concept, which seems to assume some actual relation or connection.

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value of P(p|q) is equal or close to 1, this means merely that if q would have been true, q would affirm or make probable the truth of p.

Surely, there is a distinction between the subjective judgement that some q constitutes satisfactory (relevant and convincing) evidence for some other claim p and the claim that q makes p objectively probable, in the sense that the value of P(p|q) (or P(h|e & k) analogously) reveals information or reports some fact concerning what is the case in the actual,

intersubjectively available world. In order for P(p|q) to refer to the objective probability of p given q – if the fact that P(p|q) > ½ is to say something interesting about the states of affairs in the world – q must be affirmed to be true in an intersubjective (objective) sense. In other words, it is clearly insufficient that some agent X estimates the value of P(p|q) to be high. Also, if q is to be affirmed to be true in this way, q may not refer to an event, phenomena, state of affairs internal to X, or in some other way necessarily private or bound to X.

I conclude that P(h|e & k) > ½ means merely that some observer, agent or judge has been able to formulate a P-inductive argument from a proposition e referring to some state of affairs, phenomena or event E to a proposition constituting a hypothesis h (and e is claimed to be evidence of h). In other words: there is no way of reaching a judgement of p‘s actual or objective (intersubjective) probability trough this method. Establishing that P(h|e & k) > ½ does not allow one to conclude that p is in an objective sense probable period. Rather, P(h|e & k) > ½ may at most be taken to affirm that if e was intersubjectively true, this proposition would support the truth of the further proposition h. But even this is doubtful. Bayes‘ theorem or indeed any a priori calculation of hypothetical probabilities is insensitive to the truth of e and the subjective character of (e & k).

Moreover, it seems that the application of Bayes‘ theorem in this connection (as a method of judging whether some evidence is proof of some hypothesis) assumes a subjective approach to probabilities in the sense that estimations of probability are really estimations of what it would be rational for some agent to believe. This is also the view taken on by

Horwich77. Given that the beliefs of fully rational agents conforms to the mathematical principles of probability, P(h|e & k) in Swinburne‘s logical interpretation, is most plausibly taken as a report what it would be rational for some agent X to believe if X was fully rational. This means that no matter how close to 1 Swinburne calculates the logical probability of h on e to be, he cannot conclusively prove the truth of h. Indeed, he cannot take the calculation of P(h|e & k) to say anything concerning what exists in the world.

3. Cumulative arguments

3.1 Formulating a cumulative argument

Applying the above outlined method in his attempt to prove the hypothesis of theism,

Swinburne specifies h to represent the hypothesis ―God exists‖ and takes e1,… en, to represent

the evidence of the arguments for and against the existence of God he takes up for

consideration. He takes e1 to represent the proposition that there is a physical universe so that

―P(h|e1 & k) represents the probability that God exists given that there is a physical universe

(...) and (...) mere tautological evidence [k]‖78 Together, e1,… en forms the new evidence, e, of

a cumulative P-inductive argument for h.

When first acquainted with Swinburne‘s argument, one may find his terminology confusing in the sense that one may initially find it hard judging whether it is (a.) the traditional a posteriori inductive arguments themselves or (b.) the phenomena and events these arguments take as premises, that constitute premises of his cumulative argument. Whereas it is said in ―Arguments for the existence of God‖ that

77

As I stated above

Richard Swinburne&apos;s Inductive Argument for the Existence of God – A Critical Analysis